First slide

Trigonometric transformations

Question

If $\cos (x - y) = a \cos (x + y)$ , then $\cot x \cot y$ is equal to

Moderate

A

$\frac{a - 1}{a + 1}$
B

$\frac{a + 1}{a - 1}$
C

$a - 1$
D

$a + 1$

Solution

$\begin{array}{l} \frac{\cos (x - y)}{\cos (x + y)} = a \\ \Rightarrow \frac{\cos (x - y) + \cos (x + y)}{\cos (x - y) - \cos (x + y)} = \frac{a + 1}{a - 1} \\ \Rightarrow \cot x \cot y = \frac{a + 1}{a - 1} \end{array}$

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